Mathematics of Taz
Many concepts of mathematics may be considered "Taz", in both literal value and symbolism. Numerical Taz The Middle Number The most obvious Taz concept would be the number 0.5, half of 1, which is a fundamental value in all of mathematics. It may be argued, however, that every number on the numberline is Taz of the number doubled. Similarly, 2 is a fundamental Taz value, as it equals 1/0.5. It is unclear, however, if 0.5 really is Taz of 1. Is Taz simply half of a value, or the value between both halves of it? Is it the point at which you move between 0.49 and 0.5, 0.4-recursive-9? It would also depend on whether you choose to include 0. For instance, could one say the Taz of 3 is 2 (average of 1 and 3), or 2.5 (average of 0 and 3)? The integer 0 is Taz of the positive and negative sides of the numberline, as a kind of bridge between the "worlds". Even its shape is similar to that of a round doorway. Exponential Taz On a more abstract scale, the exponential one, in which the distance from n^k to n^k+1 is equal for all values of k'', the Taz of a number would be logarithmic in nature. For instance, the Log-Taz base 2 of 256, which is ''2^8, would be 2^(8/2) = 2^4 = 16. It could also be found by the median of all integer values of k''. This is similar in functionality to a later topic, Multi-Dimensional Taz, but exponential functions are only an example to illustrate how practically ''any ''mathematical function ''f(x), when compared with x'', has a Taz point. Taz in Other Bases On the note of powers, different bases would represent numbers differently. Binary (base 2) represents 0.5 as 0.1. Similarly in the decimal system (base 10), as values after the decimal point represent ''1/10, 1/100, 1/1000, etc., values in binary represent 1/2, 1/4, 1/8, and so on, which in binary are 1/10, 1/100, and 1/1000 respectively. Hexadecimal's (base 16) equivalent of decimal's 0.5 is 0.8, half of A (16). The Taz of odd-value bases are generally long or recursive, such as 0.-recursive-2 as evident in base 5. Multi-Dimensional Taz The previous examples were all based on a 1-dimensional number line, however multi-dimensional Taz values would also exist. The Taz of a square on a cartesian plane with side lengths of 1 unit would be at the center of it, so measuring the same way as with the 1-dimensional plane from 0, you could say that a square with 0.5 units side length is Taz of a square with 1 unit side length. From this, you can conclude that the Taz of 1 unit squared is 0.25 units squared, since the formula for the area of a square is 1^2 and 0.5^2 = 0.25. Using this same logic, and knowing that the volume of a cube is 1^3, one can calculate the Taz of a cube to be 0.125 (0.5^3). This is no different for higher-dimentional "cubes", the Taz of a tesseract is 0.0625 (0.5^4) and a pentaract's Taz is 0.03125 (0.5^5). There is a simple formula for finding the Taz of an n''-dimensional cube: ''(d/2)^n, where d'' is the side length. Fractal Taz Fractals, being the mathematical concept of a repeating shape with infinite perimeter, may also be considered Taz. Generally, Taz fractals would be fractals including ratio of 0.5 in some way, however due to their unique nature compared to other fractals there is no definite line between Taz and not-Taz fractals. A simple fractal shape would be a spiral shape which halves in radius and/or width every x''% of the turn, or some variant of this idea, the Taz being the ratio of a half the radius changes by. A more famous example of a Taz fractal would be the Sierpiński series, featuring the removal of a shape from the middle (Taz) of a larger version of said shape, repeated infinitely for all remaining area. The most notable examples are the triangle (infinite Triforce), square, and 3D counterparts of them. This example does not mention any ratio of 0.5, nor do the internal shapes have to be exactly half the size of the outer, yet this fractal may be considered Taz due to the idea of a "middle". A fractal tree, generally a repeating line with at least 2 smaller identical lines growing from it may be comprehended as symbolizing all paths, left and right, converging into a single Taz, the original and source of all branches. Despite not having a literal Taz in their functions, virtually any fractal may have some concept of Taz embedded within it symbolically more than mathematically. Taz Numbers and Symbolism Symbolically, the number 555 is a mirror to Christianity's Number of the Beast, 666, showing Taz's "forbidden" uniqueness compared to other philosophies. The number three is a Taz number as it includes the sides and Taz for without the 2 sides there is no Taz. Taz is a glue that holds the sides together. The values of 0.5 and 2 are by definition linked, and are fundamental numerical values to the majority of mathematics.